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<div class="title">NumTraits.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2006-2010 Benoit Jacob &lt;jacob.benoit.1@gmail.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_NUMTRAITS_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_NUMTRAITS_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">// default implementation of digits10(), based on numeric_limits if specialized,</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">// 0 for integer types, and log10(epsilon()) otherwise.</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keyword">template</span>&lt; <span class="keyword">typename</span> T,</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;          <span class="keywordtype">bool</span> use_numeric_limits = std::numeric_limits&lt;T&gt;::is_specialized,</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;          <span class="keywordtype">bool</span> is_integer = NumTraits&lt;T&gt;::IsInteger&gt;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="keyword">struct </span>default_digits10_impl</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;{</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">int</span> run() { <span class="keywordflow">return</span> std::numeric_limits&lt;T&gt;::digits10; }</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;};</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="keyword">struct </span>default_digits10_impl&lt;T,false,false&gt; <span class="comment">// Floating point</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;{</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">int</span> run() {</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keyword">using</span> std::log10;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="keyword">using</span> std::ceil;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits&lt;T&gt;::Real Real;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <span class="keywordflow">return</span> int(<a class="code" href="namespaceEigen.html#aa73e38be0689a463ae14141b9cf89c35">ceil</a>(-<a class="code" href="namespaceEigen.html#a25256faeec3ffd0f3615a0e1e45dfb14">log10</a>(NumTraits&lt;Real&gt;::epsilon())));</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;  }</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;};</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160; </div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="keyword">struct </span>default_digits10_impl&lt;T,false,true&gt; <span class="comment">// Integer</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;{</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">int</span> run() { <span class="keywordflow">return</span> 0; }</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;};</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160; </div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160; </div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="comment">// default implementation of digits(), based on numeric_limits if specialized,</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="comment">// 0 for integer types, and log2(epsilon()) otherwise.</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="keyword">template</span>&lt; <span class="keyword">typename</span> T,</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;          <span class="keywordtype">bool</span> use_numeric_limits = std::numeric_limits&lt;T&gt;::is_specialized,</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;          <span class="keywordtype">bool</span> is_integer = NumTraits&lt;T&gt;::IsInteger&gt;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="keyword">struct </span>default_digits_impl</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;{</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">int</span> run() { <span class="keywordflow">return</span> std::numeric_limits&lt;T&gt;::digits; }</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;};</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="keyword">struct </span>default_digits_impl&lt;T,false,false&gt; <span class="comment">// Floating point</span></div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;{</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">int</span> run() {</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="keyword">using</span> std::log;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <span class="keyword">using</span> std::ceil;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits&lt;T&gt;::Real Real;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="keywordflow">return</span> int(<a class="code" href="namespaceEigen.html#aa73e38be0689a463ae14141b9cf89c35">ceil</a>(-<a class="code" href="namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>(NumTraits&lt;Real&gt;::epsilon())/<a class="code" href="namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>(<span class="keyword">static_cast&lt;</span>Real<span class="keyword">&gt;</span>(2))));</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  }</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;};</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160; </div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="keyword">struct </span>default_digits_impl&lt;T,false,true&gt; <span class="comment">// Integer</span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;{</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">int</span> run() { <span class="keywordflow">return</span> 0; }</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;};</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160; </div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="keyword">namespace </span>numext {</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="comment">// TODO: Replace by std::bit_cast (available in C++20)</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Tgt, <span class="keyword">typename</span> Src&gt;</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(<span class="keyword">const</span> Src&amp; src) {</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  <span class="comment">// The behaviour of memcpy is not specified for non-trivially copyable types</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  EIGEN_STATIC_ASSERT(std::is_trivially_copyable&lt;Src&gt;::value, THIS_TYPE_IS_NOT_SUPPORTED);</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  EIGEN_STATIC_ASSERT(std::is_trivially_copyable&lt;Tgt&gt;::value &amp;&amp; std::is_default_constructible&lt;Tgt&gt;::value,</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED);</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  EIGEN_STATIC_ASSERT(<span class="keyword">sizeof</span>(Src) == <span class="keyword">sizeof</span>(Tgt), THIS_TYPE_IS_NOT_SUPPORTED);</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  Tgt tgt;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  <span class="comment">// Load src into registers first. This allows the memcpy to be elided by CUDA.</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  <span class="keyword">const</span> Src staged = src;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  EIGEN_USING_STD(memcpy)</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  memcpy(&amp;tgt, &amp;staged, <span class="keyword">sizeof</span>(Tgt));</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  <span class="keywordflow">return</span> tgt;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;}</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;}  <span class="comment">// namespace numext</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>GenericNumTraits</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;{</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    IsInteger = std::numeric_limits&lt;T&gt;::is_integer,</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;    IsSigned = std::numeric_limits&lt;T&gt;::is_signed,</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    IsComplex = 0,</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    RequireInitialization = internal::is_arithmetic&lt;T&gt;::value ? 0 : 1,</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;    ReadCost = 1,</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    AddCost = 1,</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    MulCost = 1</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  };</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160; </div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  <span class="keyword">typedef</span> T Real;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;IsInteger, std::conditional_t&lt;<span class="keyword">sizeof</span>(T)&lt;=2, <span class="keywordtype">float</span>, <span class="keywordtype">double</span>&gt;, T&gt; NonInteger;</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  <span class="keyword">typedef</span> T Nested;</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <span class="keyword">typedef</span> T Literal;</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160; </div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> Real epsilon()</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  {</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    <span class="keywordflow">return</span> numext::numeric_limits&lt;T&gt;::epsilon();</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  }</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160; </div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">int</span> digits10()</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  {</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="keywordflow">return</span> internal::default_digits10_impl&lt;T&gt;::run();</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;  }</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160; </div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">int</span> digits()</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  {</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    <span class="keywordflow">return</span> internal::default_digits_impl&lt;T&gt;::run();</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  }</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160; </div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">int</span> min_exponent()</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  {</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    <span class="keywordflow">return</span> numext::numeric_limits&lt;T&gt;::min_exponent;</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  }</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">int</span> max_exponent()</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  {</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="keywordflow">return</span> numext::numeric_limits&lt;T&gt;::max_exponent;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  }</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160; </div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> Real dummy_precision()</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;  {</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <span class="comment">// make sure to override this for floating-point types</span></div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <span class="keywordflow">return</span> Real(0);</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  }</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160; </div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> T highest() {</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="keywordflow">return</span> (numext::numeric_limits&lt;T&gt;::max)();</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  }</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160; </div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> T lowest()  {</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    <span class="keywordflow">return</span> IsInteger ? (numext::numeric_limits&lt;T&gt;::min)()</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;                     : static_cast&lt;T&gt;(-(numext::numeric_limits&lt;T&gt;::max)());</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  }</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160; </div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> T infinity() {</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <span class="keywordflow">return</span> numext::numeric_limits&lt;T&gt;::infinity();</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  }</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160; </div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> T quiet_NaN() {</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <span class="keywordflow">return</span> numext::numeric_limits&lt;T&gt;::quiet_NaN();</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  }</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;};</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160; </div>
<div class="line"><a name="l00230"></a><span class="lineno"><a class="line" href="structEigen_1_1NumTraits.html">  230</a></span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span><a class="code" href="structEigen_1_1NumTraits.html">NumTraits</a> : GenericNumTraits&lt;T&gt;</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;{};</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160; </div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span><a class="code" href="structEigen_1_1NumTraits.html">NumTraits</a>&lt;float&gt;</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;  : GenericNumTraits&lt;float&gt;</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;{</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">float</span> dummy_precision() { <span class="keywordflow">return</span> 1e-5f; }</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;};</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160; </div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>NumTraits&lt;double&gt; : GenericNumTraits&lt;double&gt;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;{</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> dummy_precision() { <span class="keywordflow">return</span> 1e-12; }</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;};</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160; </div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>NumTraits&lt;long double&gt;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  : GenericNumTraits&lt;long double&gt;</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;{</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> dummy_precision() { <span class="keywordflow">return</span> 1e-15l; }</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;};</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160; </div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Real_&gt; <span class="keyword">struct </span>NumTraits&lt;std::complex&lt;Real_&gt; &gt;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  : GenericNumTraits&lt;std::complex&lt;Real_&gt; &gt;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;{</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;  <span class="keyword">typedef</span> Real_ Real;</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits&lt;Real_&gt;::Literal Literal;</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    IsComplex = 1,</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;    RequireInitialization = NumTraits&lt;Real_&gt;::RequireInitialization,</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    ReadCost = 2 * NumTraits&lt;Real_&gt;::ReadCost,</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;    AddCost = 2 * NumTraits&lt;Real&gt;::AddCost,</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    MulCost = 4 * NumTraits&lt;Real&gt;::MulCost + 2 * NumTraits&lt;Real&gt;::AddCost</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  };</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> Real epsilon() { <span class="keywordflow">return</span> NumTraits&lt;Real&gt;::epsilon(); }</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> Real dummy_precision() { <span class="keywordflow">return</span> NumTraits&lt;Real&gt;::dummy_precision(); }</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">int</span> digits10() { <span class="keywordflow">return</span> NumTraits&lt;Real&gt;::digits10(); }</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;};</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160; </div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> Rows, <span class="keywordtype">int</span> Cols, <span class="keywordtype">int</span> Options, <span class="keywordtype">int</span> MaxRows, <span class="keywordtype">int</span> MaxCols&gt;</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;<span class="keyword">struct </span>NumTraits&lt;Array&lt;Scalar, Rows, Cols, Options, MaxRows, MaxCols&gt; &gt;</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;{</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;  <span class="keyword">typedef</span> Array&lt;Scalar, Rows, Cols, Options, MaxRows, MaxCols&gt; ArrayType;</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits&lt;Scalar&gt;::Real RealScalar;</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;  <span class="keyword">typedef</span> Array&lt;RealScalar, Rows, Cols, Options, MaxRows, MaxCols&gt; Real;</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits&lt;Scalar&gt;::NonInteger NonIntegerScalar;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  <span class="keyword">typedef</span> Array&lt;NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols&gt; NonInteger;</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;  <span class="keyword">typedef</span> ArrayType &amp; Nested;</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits&lt;Scalar&gt;::Literal Literal;</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160; </div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;    IsComplex = NumTraits&lt;Scalar&gt;::IsComplex,</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;    IsInteger = NumTraits&lt;Scalar&gt;::IsInteger,</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;    IsSigned  = NumTraits&lt;Scalar&gt;::IsSigned,</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;    RequireInitialization = 1,</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    ReadCost = ArrayType::SizeAtCompileTime==<a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="code" href="namespaceEigen.html#a3163430a1c13173faffde69016b48aaf">HugeCost</a> : ArrayType::SizeAtCompileTime * int(NumTraits&lt;Scalar&gt;::ReadCost),</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;    AddCost  = ArrayType::SizeAtCompileTime==<a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="code" href="namespaceEigen.html#a3163430a1c13173faffde69016b48aaf">HugeCost</a> : ArrayType::SizeAtCompileTime * int(NumTraits&lt;Scalar&gt;::AddCost),</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    MulCost  = ArrayType::SizeAtCompileTime==<a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="code" href="namespaceEigen.html#a3163430a1c13173faffde69016b48aaf">HugeCost</a> : ArrayType::SizeAtCompileTime * int(NumTraits&lt;Scalar&gt;::MulCost)</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;  };</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160; </div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar epsilon() { <span class="keywordflow">return</span> NumTraits&lt;RealScalar&gt;::epsilon(); }</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar dummy_precision() { <span class="keywordflow">return</span> NumTraits&lt;RealScalar&gt;::dummy_precision(); }</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160; </div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">int</span> digits10() { <span class="keywordflow">return</span> NumTraits&lt;Scalar&gt;::digits10(); }</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;};</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160; </div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>NumTraits&lt;std::string&gt;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  : GenericNumTraits&lt;std::string&gt;</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;{</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    RequireInitialization = 1,</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    ReadCost = <a class="code" href="namespaceEigen.html#a3163430a1c13173faffde69016b48aaf">HugeCost</a>,</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;    AddCost  = <a class="code" href="namespaceEigen.html#a3163430a1c13173faffde69016b48aaf">HugeCost</a>,</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    MulCost  = <a class="code" href="namespaceEigen.html#a3163430a1c13173faffde69016b48aaf">HugeCost</a></div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  };</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160; </div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">int</span> digits10() { <span class="keywordflow">return</span> 0; }</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160; </div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> std::string epsilon();</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> std::string dummy_precision();</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> std::string lowest();</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> std::string highest();</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> std::string infinity();</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> std::string quiet_NaN();</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;};</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160; </div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;<span class="comment">// Empty specialization for void to allow template specialization based on NumTraits&lt;T&gt;::Real with T==void and SFINAE.</span></div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>NumTraits&lt;void&gt; {};</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160; </div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>NumTraits&lt;bool&gt; : GenericNumTraits&lt;bool&gt; {};</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160; </div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160; </div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_NUMTRAITS_H</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a25256faeec3ffd0f3615a0e1e45dfb14"><div class="ttname"><a href="namespaceEigen.html#a25256faeec3ffd0f3615a0e1e45dfb14">Eigen::log10</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log10_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log10(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a3163430a1c13173faffde69016b48aaf"><div class="ttname"><a href="namespaceEigen.html#a3163430a1c13173faffde69016b48aaf">Eigen::HugeCost</a></div><div class="ttdeci">const int HugeCost</div><div class="ttdef"><b>Definition:</b> Constants.h:46</div></div>
<div class="ttc" id="anamespaceEigen_html_aa73e38be0689a463ae14141b9cf89c35"><div class="ttname"><a href="namespaceEigen.html#aa73e38be0689a463ae14141b9cf89c35">Eigen::ceil</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_ceil_op&lt; typename Derived::Scalar &gt;, const Derived &gt; ceil(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:24</div></div>
<div class="ttc" id="anamespaceEigen_html_ae8bb75ba4f5f30a7571146dbfa653c6d"><div class="ttname"><a href="namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">Eigen::log</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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